At the official EVE Online site, Oveur has posted some information regarding the startup problems that some have been experiencing:
We've been adding hardware to the server cluster in the last weeks. Today, we added the latest batch of servers and due to the patch problems we had to deploy certain server-side hotfixes. Problems arose in startup, after which we started rolling back the server-side hotfixes and then the hardware to isolate the problem. We sincerely apologize for the inconvenience and hope you understand our urgency in adding both hardware and server-side hotfixes to address the issues on Tranquility.
I had a few problems earlier this week, but I cleared out my cache and it seemed to fix them. If you do that, make sure to back up your settings and preferences.
